Pierre-François Koehl

Optimal Investment Strategies in the presence of a Minimum Guarantee.

In a continuous-time framework, we consider the problem of a De…ned Contribution Pension Fund in the presence of a minimum guarantee. The problem of the fund manager is to invest the initial wealth and the (stochastic) contribution ‡ow into the …nancial market, in order to maximize the expected util- ity function of the terminal wealth under the constraint that the terminal wealth must exceed the minimum guarantee. We assume that the stochastic interest rates follow the a¢ne dynamics, including the CIR (Cox, Ingersoll and Ross 1985) model and the Vasiµ model. The optimal investment strategies are obtained by assum- ing the completeness of …nancial markets and a CRRA utility function. Explicit formulae for the optimal investment strategies are included for dierent examples of guarantees and contributions.

Conditional dominance criteria: definition and application to risk-management

Abstract We define the concept of conditional dominance and use it for obtaining bounds on the hedging prices of random variables. These bounds depend only on the characteristics of the financial market and the random variables to hedge. Moreover, they are coherent with the equilibrium and tighter than the ones obtained by the classical super-replication approach, significantly in some cases. This approach can be applied in static as well as dynamic frameworks.